Motion and Force

Chapter Twelve: Distance, Time, and Speed 12.1 Distance, Direction, and Position 12.2 Speed 12.3 Graphs of Motion

Standards for Today: Motion: 1. The velocity of an object is the rate of change of its position. a. position is defined relative to some choice of standard reference point and a set of reference directions. b. average speed is the total distance traveled divided by the total time elapsed. The speed of an object along the path traveled can vary.

c. how to solve problems involving distance, time, and average speed. d. to describe the velocity of an object one must specify both direction and speed. e. changes in velocity can be changes in speed, direction, or both. f. how to interpret graphs of position versus time and speed versus time for motion in a single direction.

12.3 The position vs. time graph Motion graphs are an important tool used to show the relationships between position, speed, and time. A runner can learn more about performance by studying data and graphs.

12.3 The position vs. time graph Position vs. time data tells you the runner’s position at different points in time. The runner is at 50 meters after 10 sec., 100 meters after 20 sec. and 150 meters at 30 sec.

12.3 Graphs show relationships A good way to show a relationship between two variables is to use a graph. A graph makes it easy to see if changes in one variable cause changes in the other variable (the effect).

12.3 The position vs. time graph To graph data, you put position on the vertical (y) axis . Time goes on the horizontal (x) axis. Data are plotted between x and y axis.

12.3 The position vs. time graph An object moving at a constant speed always creates a speed vs. time graph that is a straight line.

12.3 The position vs. time graph Two variables may have: a strong relationship, a weak relationship, or no relationship at all.

12.3 Graphs show relationships This table shows how quickly the car gets from A to B as the angle of the track changes.

12.3 Graphs show relationships If we plot the data on a graph, what kind of relationship does the graph show?

12.3 Four steps to make a graph Step 1: Choose which will be the dependent and independent variables. The dependent variable goes on the y-axis and the independent variable goes on the x-axis. Step 2: Make a scale for each axis by counting boxes to fit your largest value. Count by multiples of 1, 2, 5, or 10. Step 3: Plot each point by finding the x-value and drawing a lin upward until you get to the right y-value. Step 4: Draw a smooth curve that shows the pattern of the points. Do not just connect the dots.

12.3 Reading a graph A graph can give you an accurate answer even without doing the experiment. Students doing an experiment measured the speed of the car at 20, 40, 60, and 80 cm positions. They want to know the speed at 50 cm.

12.3 Slope You can use position vs. time graphs to quickly compare the speeds of different objects. A steeper line on a position vs. time graph means a faster speed.

12.3 Slope The “steepness” of a line is called its slope. Visualize a triangle with the slope as the hypotenuse. The rise is equal to the height of the triangle. The run is equal to the length along the base of the triangle.

12.3 Slope The slope is the ratio of the “rise” (vertical change) to the “run” (horizontal change). The slope is therefore a distance divided by a time, which equals speed.

12.3 Speed vs. time graphs The position vs. time graph has position on the y-axis and time on the x-axis. Which runner has the fastest constant speed?

12.3 Speed vs. time graphs These graphs each show the same event. What differences do you notice?

Do these graphs display the same data?

12.3 Calculating distance A speed vs. time graph can also be used to find the distance the object has traveled.